Known Rarities: [In order of rarity]
{Seraph}

Ultra_White [>9]
Efervescent [9]
BE_White [8]
Ultra_Pearlescent [7]
Ultra_Purple [6]
AS_White [5]
Seraph [4]
Pearlescent [3]
Gold [~:2]
{Regular}
Black [>11]
AL_White [11]
Legendary [7:10]
Etech [6]
BE_Legendary [5]
Purple [4]
Blue [3]
Green [2]
White [1]
Grey [~]

Numbers contained within [ and ] are points, these points are a logistic construct I have developed to explain where rarities exist, I have used these points to figure out different ways to create these rarities. Also '~' means '0' and below.

Two parts make a difference to the rarity of a weapon:
~ Body
~ Barrel

Body:
Each body level adds more points:
No Body = 0
Body with no following = 1
Body A or 3 = 2
Body B or 4 = 3
Body C or 5 = 4
Body 6 = Pearlescent, same set of rarities as seraph but +1.

Barrel:
Etech/Alien barrels will increase the rarity by 2 points.
Legendary barrels will increase the rarity by 5 points.
Seraph barrels will cause an entirely different set of rarities

This section will define what each part in a class mod does. It will not focus soley on rarity.
Parts in question:
~ Type
~ Alpha
~ Beta, Gamma, and Material

Type:
Type gives 5 points if legendary.

Alpha:
This is the specialisation base type. It defines the base rarity of the class mod
The number next to each part of the skill adds skill points based on the SX values.

X=1, 2, or 3;
Spec_Legendary = 8 (Legendary)
Spec_ASX_(-)BSX_(-)CSX = 4 (Purple)
Spec_ASX_BSX = 3 (Blue)
Spec_ASX = 2 (Green)
Spec_NoSkill = 1 (White)
No Alpha = 0

Changes to skill values:
Purple: A = +2, B = +1, C = +0
Blue: A = +3, B = +2

Therefore Etech is Blue + Blue

Beta, Gamma, and Material:
This adds to the attributes on the class mod. (E.g. Shield recharge delay)
X=0,1,2,3,4, or 5
Beta: PrimaryStat_AX_B0_C0
Gamma: PrimaryStat02_A0_BX_C0
Material: StatPenalty_A0_B0_CX

A is the first attribute, B is the second attribute, C doesn't seem to do anything.

Shield parts that influence rarity:
~ Type
~ Delta
~ Material

Type:
Seraph type gives a new set of rarities.

Delta:
Deltas are the special effects of shields. Legendary accessories will increase the rarity by 5 points.

Material:
The Material is what influences the stats and rarity the most out of any part of the shield.
Rarity Increases:
No material = 0
Common = 1
Uncommon = 2
Rare = 3
VeryRare = 4
Legendary = 5

Note: Either the material alone and not the delta will be responsible for most legendary shields as they are usually BE_Legendary and not true Legendary (5 + 5 = Legendary, 5 + 0 = BE_Legendary)
True legendary shields will have both 5 points from delta and 5 from material.

Parts that influence rarity:
~ Type
~ Epsilon

Type:
Legendary Types increase rarity by 5.
Seraph Types give a new set of rarities.

Epsilon:
This is the damage part, it will dictate the rarity of the grenade.
No Epsilon = 0
1 or 2 = 1
2 or 3 = 2
4 or 5 = 3
6 or 7 = 4

Parts that influence rarity:
~ Type
~ Eta
~ Theta

Type
Some Seraph relics use the Type instead of the Theta to create a seraph rarity.

Eta:
Legendary Eta adds 5 points

Theta:
No Theta = 0
Theta 1-3 = 1
Theta 4-7 = 2
Theta 8-11 = 3
Theta 12-15 = 4
Seraph Relic Thetas give a new set of rarities.

While most special parts conform to the rules above, some do not. I will try to list all the ones I find here.

Legendary:
Fabled Tortoise

Seraph:
Might of the Seraphs (Uses Type)
All Other Relics (Uses Theta)